Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C9⋊(#733⋊C2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C9⋊(#733⋊C2) |
| unambiguous semidirect product | #733⋊D9 |
| Fitting, derived, Sylow | C9×#733 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×#733 | C2 |
| Frattini | C33 | C3⋊(C3⋊D3) |
| socle | C32 | C3⋊#272 |
| LCS | G ▷ C9×#733 | |
| UCS | C1 | |
238 conjugacy classes of subgroups.
| transitive degree | μt(G) = 243 |
Polycyclic presentation:
2,3^6|b^3=f,c^3=g^2,d^3=fg,b^a=b^2f^2,c^a=c^2g,d^a=d^2f^2g^2,e^a=eg^2,f^a=f^2,g^a=g^2,c^b=ce,e^b=eg81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1081);